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Write abstract of Runge Kutta Method and Runge Kutta Fehlberg Method.

Define local truncation error.

What is difference between local error and global error?

Define Local Error and Global Error.

Q.Briefly describe Error analysis in Runge kutta Fehlberg method.

Q.Briefly describe Error analysis in Euler method and Taylor series method.

Q.Briefly describe Euler method and Taylor series method.

Q. Prove Taylor series method.

Q. Prove Euler Method from taylor series method.

Q. Use Runge Kutta Fehlberg method with tolerance TOL=〖10〗^(-6), hmax=0.5, and hmin=0.05 to approximate the solutions to the following initial value problem. Compare the result to the actual value.

y^'=(t+〖2t〗^3)y^3-ty, 0≤t≤2,y(2)=1, y(0)=1/3 , actual solution y(t)=〖(3+2t^2+6e^(t^2 ))〗^(-1⁄2)

y^'=(t+〖2t〗^3)y^3-ty, 0≤t≤2,y(2)=1, y(0)=1/3 , actual solution y(t)=〖(3+2t^2+6e^(t^2 ))〗^(-1⁄2)